Morsell grabbed eight rebounds and Adala Moto made 10 of 12 free-throw attempts.
Towson trailed 39-34 at halftime, but took a 43-41 lead in the opening minutes of the second half as William & Mary went three-plus minutes without a field goal. William & Mary had another drought, this time six-plus minutes, and Towson went on a 10-0 run for a 64-54 lead.
Byron Hawkins added 13 points for Towson (10-4), which was just 2 of 12 from 3-point range, but made 22 of 27 free throws.
Prewitt made two free throws with 1:09 remaining to pull within 68-65 but Towson made 8 of 10 free throws to seal it.